Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
if n == 1:
    print("NO")
else:
    a = [1]
    b = 1
    while a[-1] < n:
        b += 1
        a.append(int(b * (b + 1) / 2))
    a = a[:-1]
    r = b - 2
    l = 0
    while r != l and a[l] + a[r] != n:
        if a[l] + a[r] > n:
            r -= 1
        else:
            l += 1
    if a[l] + a[r] == n:
        print("YES")
    else:
        print("NO")